Theorems · Definition · sequences and series

tsum

{α : Type u_4} →
  {β : Type u_5} →
    [AddCommMonoid α] →
      [TopologicalSpace α] → (β → α) → optParam (SummationFilter β) (SummationFilter.unconditional β) → α

∑' i, f i is the unconditional sum of f if it exists, or 0 otherwise. More generally, if L is a SummationFilter, ∑'[L] i, f i is the sum of f with respect to L if it exists, and 0 otherwise. (Note that even if the unconditional sum exists, it might not be unique if the topology is not separated. When the support of f is finite, we make the most reasonable choice, to use the sum over the support. Otherwise, we choose arbitrarily an a satisfying HasSum f a. Similar remarks apply to more general summation filters.)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Defs

Cited by

1,148 results in Mathlib

Foundations

Depth 74 from the axioms, rests on 1,106 definitions · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpace